Reaserch On Ito Stochastic Differential Equation And Its Application In Electric Power System

In the actual engineering, with improving of model accuracy and practical problem complexity, more and more uncertain factors are considered in the model establishment. By introducing random factors on differential equation, stochastic differential equation is formed. With the development of science and technology, stochastic differential equations are more and more used in engineering.In the thesis, mathematics methods and strategies are used to analyze the problem in the power system. By establishing the corresponding stochastic differential equation, drawing the mathematics essence, analyzing the digital characteristic and deriving relevant formulae and properties, the problems are analyzed and the system is controlled.The main work of the thesis is as following:1 , The physical background is studied, and the mathematics essence is drawn. The corresponding Ito stochastic differential equations are given by introducing the random factors that really exist on original physical model, and its characteristic is studied.2, On the basis of Ito integral and FPK equation, the probability distribution of system relative power angle stabilization is studied.3 , On the basis of the nonlinear Ito stochastic differential equation models, many kinds of methods are used to solve its moment equation, and stability condition of the first moment and the second moment. The stability references of the system are provided. 4, The first-passage time problem of the system is studied by using theories of Hamilton system and Ito stochastic differential. And the security probability functionin given the initial condition is analyzed.5, Simulation of the system is studied based on Monte Carlo method and some random simulation methods. And some computing methods of stochastic differential equation are given.